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Record W4235663823 · doi:10.1142/s0129167x11007318

RANK ONE CONNECTIONS ON ABELIAN VARIETIES

2011· article· en· W4235663823 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueInternational Journal of Mathematics · 2011
Typearticle
Languageen
FieldMathematics
TopicAlgebraic Geometry and Number Theory
Canadian institutionsMcGill University
Fundersnot available
KeywordsMathematicsAbelian groupLine bundleRank (graph theory)Abelian varietyVector bundlePrincipal bundlePure mathematicsConnection (principal bundle)Variety (cybernetics)Moduli spaceAlgebra over a fieldCombinatoricsGeometry

Abstract

fetched live from OpenAlex

Let A be a complex abelian variety. The moduli space [Formula: see text] of rank one algebraic connections on A is a principal bundle over the dual abelian variety A ∨ = Pic 0 (A) for the group [Formula: see text]. Take any line bundle L on A ∨ ; let [Formula: see text] be the algebraic principal [Formula: see text]-bundle over A ∨ given by the sheaf of connections on L. The line bundle L produces a homomorphism [Formula: see text]. We prove that [Formula: see text] is isomorphic to the principal [Formula: see text]-bundle obtained by extending the structure group of the principal [Formula: see text]-bundle [Formula: see text] using this homomorphism given by L. We compute the ring of algebraic functions on [Formula: see text]. As an application of the above result, we show that [Formula: see text] does not admit any nonconstant algebraic function, despite the fact that it is biholomorphic to (ℂ*) 2 dim A implying that it has many nonconstant holomorphic functions.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.186
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0020.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.086
GPT teacher head0.308
Teacher spread0.222 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it